Game Theory is basically the mathematics of strategy, where the primary theory says that if all the players of a game play the best, most rational strategy, the resulting outcome of the game is predictable. There are plenty of economists, portfolio managers and financial advisors that employ a variation of the Game Theory model to trade and invest.

This started me thinking about the role Game Theory plays when trading the markets. Can we really say that all the players play the best, most rational strategy? Is “playing to win” really the way to go? If we play “not to lose,” do we have a greater chance of winning in the end?

I think that the players in the “Market Game” are not always rational, and this really throws off the accuracy of prediction. Attempts to use rational strategy to predict outcomes in an irrational game, tends to work until Mr. irrational behavior sits down at the table to play. Then the modeled prediction can change dramatically.

A good example of this may very well be going on right now.

It seems to me that we have arrived at the conclusion that the risk of not being “in the market” is greater than the risk of actually being in the market.  Now, think about that. If you are not involved you have no risk, so how can it be greater than the real risk of being involved? This is academic drivel. This implies that you “need” the perceived gains to keep up with inflation and the Jones’s.

As I mentioned in a previous post, Mark Hulbert at market watch was quoted as saying “Based on the several hundred investment advisers I track, I’d have to say that bullish sentiment is approaching dangerously high levels. Consider the Hulbert Stock Newsletter Sentiment Index (HSNSI), which represents the average recommended stock market exposure among a subset of short term stock market timers tracked by the Hulbert Financial Digest. 

The Hulbert Index currently stands at 62.8%, up from 13.8% just one month ago. That’s an awfully big jump for so short a period of time, suggesting that equity managers in general are more fearful of “missing out” than they are of a reasonable correction. This is evidence of overconfidence in the outcome, and although sometimes irrational behavior pays off in the markets, it usually results in a mistake.

As Shakespeare said, “To be, or not to be: that is the question: Whether ’tis nobler in the mind to suffer the slings and arrows of outrageous fortune, Or to take arms against a sea of troubles”

Peter Bernstein talks about this behavior in his book Against The gods. He says that in the early 70’s “portfolio managers became so enamored with the idea of growth in general, and the so-called Nifty Fifty growth stocks in particular, that they were willing to pay any price at all for the privilege of owning shares in companies like Xerox, Coca-Cola, IBM and Polaroid. These investment managers defined the risk in the Nifty Fifty, not as the risk of overpaying, but as the risk of not owning them.” In January 1973, the Nifty Fifty slipped into the biggest stock market decline since the Great Depression.

The point here is not to judge the current market valuations as much as it is to keep us cognizant of why we are involved in this stock market. Are we in because we think not being in is a greater risk? To me this is the ultimate “playing to win” mentality and has a tendency to blindside us if we’re wrong. The stock market is not grossly overvalued but it is not a great buying (or holding) opportunity either.

When “not being in” is a reason to own, it’s basically saying that we’re sure of the outcome. It’s the “new risk”, a destructive impulse that re-defines risk as the chance you take when you fail to bet on a sure thing. Playing to win may be the way to go in some games but not trading. I think in games like poker and trading “playing not to lose” makes better sense. Wait for the right hand so to speak, based on the cards at hand and not any other reason. When we make decisions based on emotion, when worry and caution become a vice instead of a virtue, trouble is about to pay us a visit.

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According to Wikipedia, “A game of chance is a game whose outcome is strongly influenced by some randomizing device, and upon which contestants may or may not wager money or anything of monetary value. Common devices used include dice, spinning tops, playing cards, roulette wheels or numbered balls drawn from a container. Any game of chance that involves anything of monetary value is gambling. Thus, every gamble is a game of chance, but not every game of chance is a gamble.”

So, not all games of chance are alike?

First there’s skill.

Well, unlike dice or the roulette wheel there are some games of chance that require a skill, like handicapping horses or trading. In essence, the roulette wheel is ultimately fate, where trading is a choice. A game where a person can polish their skills and make choices has a great advantage over a person who places a bet against certain odds, and waits for fate. After all, there are a number of professionals that make a living as card players or traders, yet few make a career out of throwing dice.

Then there’s time.

All games of chance are dominated by time. As Peter Bernstein puts it in his book “Against The Gods- The Remarkable Story Of Risk,” “Gamblers think they are betting on red or seven but in reality they are betting on the clock. The loser wants a short run to look like a long run so the odds will prevail. The winner wants a long run to look like a short run so the odds will be suspended.”

He goes on to say, “Insurance companies conduct their affairs in the same fashion. They set their premiums to cover the losses they will sustain in the long run; but when earthquakes and fires and hurricanes all happen around the same time, the short run can be very painful.”

Well, that sounds familiar to a trader. Good traders know they must also be properly capitalized for the short run surprises to insure long run success. As Bernstein says, “Time is the dominant factor in gambling. Risk and time are opposite sides of the coin, for if there were no tomorrow there would be no risk. Time transforms risk, and the nature of risk is shaped by the time horizon: the future is the playing field.”

Then there’s choice.

In those games of chance where fate prevails, decisions are irreversible. We place the bet down on red and that’s it. There’s no going back. In trading however, we can sell something we just bought if we feel we made a mistake. Bernstein points out that Hamlet once said too much hesitation in the face of uncertainty is bad, “yet once we act, we forfeit the option of waiting until new information comes along. As a result, not-acting has value. The more uncertain the outcome, the greater may be the value of procrastination. Hamlet had it wrong: he who hesitates is half way home.”  

Hone your skills, respect time in the game and use your ability to choose, or use the rabbits foot. Remember however, that didn’t work out so well for the rabbitt.

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Jacob Bernoulli, the famous Swiss mathematician, is best known for his introduction of the theorem known as the law of large numbers. Wikipedia defines the law of large numbers as “a theorem in probability that describes the long-term stability of the mean of a random variable. Given a random variable with a finite expected value, if its values are repeatedly sampled, as the number of these observations increases, the sample mean will tend to approach and stay close to the expected value (the average for the population).”

In other words, since the probability of flipping a coin and seeing a head (or tail) is 50%, the more we flip the coin, the more we will see the frequency of heads or tails approach 50%. Also, the expected value (50%) becomes more reliable the more we flip.

In his book “Against the Gods”, Peter L. Bernstein points out where Bernoulli performed various studies using marbles to conclude that a sample of 25,500 trials was necessary to achieve what he called “moral certainty.” Moral certainty he defines as a 2% chance of error.

He understood that the Law of Large Numbers is very important because it stabilizes long term outcomes for random events. In Las Vegas a player may beat the table in a given day, but eventually, whatever edge is built into the game will dominate, the more the game is played.

Is this true of trading systems though? I don’t think so.

First, there are big differences in reliability when testing such things as trading concepts and coin tosses. In the “real world” there are few longer term trading systems that can even produce 25,000+ trades as a sample size. Even if we could, Bernoulli had the advantage of working with a closed sample (5,000 marbles). Traders take in new data every day as new trades surface. This is the equivalent of throwing more marbles in the jar, perhaps even different colored marbles. Although a back test with 5,000 trades is likely to be more reliable than one with 200, it still has limitations that should be viewed with skepticism.

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